Basically what is in the title; I suspect that I need to update the motherboard's BIOS to a more current version, but that would require me getting another processor just to do that. I want to make sure that I'm right before I do anything like that.
The CPU is supported (F3 required for 4.1 revision boards). The F3 was released in October 2012, so your board should be good.
http://www.gigabyte.com/products/product-page.aspx?pid=4305#bios.
For 5.0 revision boards it's supported from the first BIOS release.